لخّصلي

MEASUREMENT AND UNITS
Dr. Auday K.
4/22/2024 DR. AUDAY K.A. 1
Measurement is a technique by means of which we attach a number to a
physical or chemical property as a result of comparing it, with a similar,
standard, quantity that has been adopted as a unit.
The measurement of physical or chemical quantities requires:

1. The standard or unit in which the quantity is measured.


2. The numerical value representing the number of times the quantity
   contains that unit.
   Measurement
   Measurement
   units of
   dimensional
   quantities
   Units dimensions
   (Numerical value)
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   A number indicates “how much,” but
   the unit indicates “of what.” The “of
   what” is important when
   communicating a quantity.
   MEASUREMENTS
   FUNDAMENTAL AND DERIVED UNITS
   The physical quantities which do not
   depend upon other quantities are called
   fundamental quantities (in M.K.S.C.
   system the fundamental quantities are
   length, mass, time and charge).
   The units of fundamental quantities are
   called fundamental units.
   The units of physical or chemical
   quantities which may be derived from
   fundamental units are called derived
   units.
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   PRINCIPAL SYSTEMS OF UNITS
   C.G.S. System: In this system the unit
   of length is cm, that of mass is gm
   and that of time is second.
   F.P.S. System (The British System): In
   this system the unit of length, mass
   and time are foot (f), pound (Ib) and
   second (s) respectively.
   M.K.S.C. System: In this system the
   units of length, mass, time and charge
   are meter (m), kilogram (kg), second
   (s) and charge (c) respectively.
   S.I. System (International System of
   Units or Metric system): In this system
   there are seven fundamental
   quantities whose units and symbols
   are given in a table.
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   S.N. Fundamental
   quantity
   Unit Symbol

1. Length meter m


2. Mass kilogram kg


3. Time second s


4. Temperature kelvin K


5. Luminous Intensity candela cd


6. Electric Current ampere A


7. Amount of Substance mole mol
   UNIT PREFIXES
   In addition to the basic SI units, we
   can also use other units, such as
   millimeters and nanoseconds, where
   the prefixes milli- and nano- denote
   various powers of ten. For example,
   the prefix “kilo-” abbreviated k,
   always means a unit larger by a
   factor of 1000; thus
   1 kilometer = 1 km = 103
   meters = 103 m
   1 kilowatt = 1 kW = 103 watts
   = 103 W
   The 20 SI prefixes used form decimal
   multiples and submultiples of SI units
   are listed in a table.
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   Prefixes for SI Units
   Power Prefix
   abbrev
   iation
   Power Prefix
   abbrev
   iation
   10-24 yocto y 101 deka da
   10-21 zepto z 102 hecto h
   10-18 atto a 103 kilo k
   10-15 femto f 106 mega M
   10-12 pico p 109 giga G
   10-9 nano n 1012 tera T
   10-6 micro μ 1015 peta P
   10-3 milli m 1018 exa E
   10-2 centi c 1021 zetta Z
   10-1 deci d 1024 yotta Y
   قائمة السوابق في النظام الدولي للوحدات
   CONVERSION OF UNITS
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   Sometimes it is necessary to convert units from one system to another. Conversion factors
   between the SI units and conventional units of length are as follows:
   1 mi = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm
   1 m = 39.37 in.= 3.281 ft 1 in. = 0.025 4 m = 2.54 cm
   Units can be treated as algebraic quantities that can cancel each other. For example,
   suppose we wish to convert 15.0 in. to centimeters. Because 1 in. is defined as exactly
   2.54 cm, we find that
   15.0 in. = (15.0 in.)(2.54 cm/in.) = 38.1 cm
   This works because multiplying by (2.54 cm/in.) is the same as multiplying by 1, because
   the numerator and denominator describe identical things.
   4/22/2024 DR. AUDAY K.A. 7
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   Example: The Density of a Cube
   The mass of a solid cube is 856 g, and each edge has a length of 5.35 cm. Determine the
   density of the cube in basic SI units.
   Solution:
   Because 1 g =10-3 kg and 1 cm = 10-2 m, the mass m and volume V in basic SI units are
   𝑚 = 856𝑔 × 10−3𝑘𝑔
   𝑔
   = 0.856 𝑘𝑔
   𝑉 = 𝐿3 = (5.35 𝑐𝑚 × 10−2𝑚/𝑐𝑚)3= (5.35)3× 10−6𝑚3 = 1.53 × 10−4𝑚3
   Therefore,
   𝜌 =
   𝑚
   𝑉
   =
   0.856 𝑘𝑔
   1.53 × 10−4𝑚3
   = 5.59 𝑘𝑔/𝑚3
   Example: Converting feet to meters.
   The height of a building is 100.0 ft. Find the height in meters.
   Solution:
   To express the height h in meters, multiply the height in feet by the conversion factor
   that converts feet to meters, that is,
   ℎ = 100.0 𝑓𝑡 1 𝑚
   3.281 𝑓𝑡
   = 30.48 𝑚
   Example: Express the time T of one day in terms of seconds.
   Solution:
   𝑇 = 1 𝑑𝑎𝑦
   24 ℎ𝑟
   1 𝑑𝑎𝑦
   60 𝑚𝑖𝑛
   1 ℎ𝑟
   60 𝑠𝑒𝑐
   1 𝑚𝑖𝑛
   = 86400 𝑠𝑒𝑐.
   UNCERTAINTIES
   Chemistry and physics are a quantitative sciences and that means a lot
   of measurements and calculations.
   Laboratory investigations involve taking measurements of physical and
   chemical quantities, and the process of taking any measurement always
   involves some uncertainty or experimental error.
   We refer to the uncertainty as the error in the measurement.
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   Types of
   Experimental
   Uncertainty
   Random or
   Statistical Error
   (indeterminate
   error)
   Personal
   error
   Systematic Error
   (determinate error)
   RANDOM OR STATISTICAL ERRORS
   These errors result from unknown and unpredictable
   variations in experimental situations.
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   Conditions in which random errors can result:
   1- Unpredictable fluctuations in temperature or line
   voltage.
   2- Mechanical vibrations of the experimental setup.
   Reduce and minimize Random errors:
   The effect of random errors may be reduced and minimized by improving and refining
   experimental techniques
   PERSONAL ERRORS
   Personal error arises from personal bias or carelessness
   in reading an instrument, in recording observation, or in
   mathematical calculations.
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   Examples of personal errors include:
   1- Errors in reading a scale. The alignment (the
   value of the reading) can depend on the position
   of the eye (parallax).
   2- Not observing significant figures in
   calculations.
   SYSTEMATIC ERRORS
   Conditions from which systematic errors can
   result include:
   1- An improperly zeroed instrument (e.g. balance or
   ammeter).
   2- A thermometer that reads 101 ºC when
   immersed in boiling water at standard atmospheric
   pressure. The thermometer is improperly calibrated
   since the reading should be 100 ºC.
   3- A meter stick that has shrunk due to
   environmental conditions would always read
   higher.
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   Systematic errors are errors associated with particular measurement
   instruments or techniques, such as an improperly calibrated instrument or bias
   on the part of the observer.
   Avoiding systematic errors depends on the skill of the
   observer to recognize the sources of such error and to
   correct them.
   ACCURACY & PRECISION
   Accuracy:
    How close individual measurements agree
   with true value (is the degree of veracity).
    Depends on the person measuring.
    The less difference between the measured
   values and true value gives more
   accuracy.
    Calculated by the formula:
   % Error = (YV – AV) x 100 ÷
   AV
   Where: YV is YOUR measured Value
   & AV is the Accepted Value
   Precision:
    How close individual measurements agree (is
   the degree of reproducibility).
    Depends on the measuring tool.
    The less difference between the measured
   values gives more precision.
    Determined by the number of significant
   digits
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    Accuracy & Precision may be demonstrated by shooting at a target.
    Accuracy is represented by hitting the bulls eye (the accepted value)
    Precision is represented by a tight grouping of shots (they are finely tuned)
   Accuracy & Precision
   Precision without
   Accuracy
   No Precision &
   No Accuracy
   Accuracy without
   Precision
   4/22/2024 DR. AUDAY K.A. 14
   ACCURACY - CALCULATING % ERROR
   If a student measured the room width at 8.46 m and the accepted value was 9.45 m what was their accuracy?
   Using the formula: % error = (YV – AV) x 100 ÷ AV
    Where YV is the student’s measured value & AV is the accepted value
   Since YV = 8.46 m, AV = 9.45 m
   % Error = (8.46 m – 9.45 m) x 100 ÷ 9.45 m
   = -0.99 m x 100 ÷ 9.45 m
   = -99 m ÷ 9.45 m
   = -10.5 %
    Note that the meter unit cancels during the division & the unit is
   %. The (-) shows that YV was low
   The student was off by almost 11% & must remeasure
   Acceptable % error is within 5%
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   remeasure -5%
   +5% remeasure
   Acceptable error is +/- 5%
   Values from –5% up to 5% are acceptable
   Values less than –5% or greater than 5% must be remeasured
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   • By convention, a measurement is recorded by writing all exactly known numbers and 1
   number which is uncertain, together with a unit label.
   • All numbers written in this way, including the uncertain digit, are called significant figures.
   • A certain number of figures depends on the least count of instrument scale, which is the
   smallest subdivision on the measurement scale.
   • For example, the blue line is 2.73 cm long. This measurement has 3 significant figures. The
   first 2 digits (2.7 cm) are exactly known. The third digit (0.03 cm) is uncertain because it was
   interpolated or estimated 1 digit beyond the smallest graduation.
   LEAST COUNT AND SIGNIFICANT FIGURES
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   DR. AUDAY K.A.
   The confirmed and the estimated number with the following rules:
   • Non – zero digits are always significant
   • Zeros between nonzero digits are significant. That is, 508 cm has 3 significant figures.
   • Leading zeroes merely locate the decimal point and are never significant. That is, 0.0497 cm
   equals 4.97 x 10-2 cm and has 3 significant figures.
   • Numbers that have one or more zeros at the end without a decimal point, and if the last zero is
   the estimated digit then we can use scientific notation to write these numbers. 93,000,000
   miles equal 9.300x107 mi.
   • Trailing zeros are significant as follows: 50.0 mL has 3 significant figures, 50. mL has 2
   significant figures, and 50 mL has 1 significant figure.
   SIGNIFICANT FIGURES AND ZEROS
   Datum
   (grams)
   Number of
   Significant
   Figures
   Datum
   (milliliters)
   Number of
   Significant
   Figures
   10,034
   1.908
   0.32
   0.00046
   150
   0.0000160

0.705
0.054
5.86 x 10-7
3040
0.109800
5
4
2
2
2
3
3
3
2
3
3
6
4/22/2024 18
DR. AUDAY K.A.
• When adding or subtracting do NOT extend the result beyond the first
column with a doubtful figure. For example, …
SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION
4/22/2024 19
DR. AUDAY K.A.
• What is 16.874 + 2.6?
• What is 16.874 - 2.6?
SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION
4/22/2024 20
DR. AUDAY K.A.
• When multiplying or dividing the answer will have the same number of
significant digits as the least accurate number used to get the answer. For
example, …
2.005 g / 4.95 mL = 0.405 g/mL
• What is 16.874 x 2.6?
• What is 16.874 / 2.6?
SIGNIFICANT FIGURES, MULTIPLICATION, AND DIVISION
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DR. AUDAY K.A.